matrix. Depending on the columns removed, the answer will differ by multiplication by , where the power of is not necessarily the number of crossings in the knot. To resolve this ambiguity, divide out the largest possible power of and multiply by if necessary, so that the constant term is positive. This gives the Alexander polynomial. For example, this shows immediately that the Alexander polynomial of the unknot is 1 (though this follows also immediately from the definition).

The Alexander polynomial